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We experimentally investigate the fluidization of a granular material subject to mechanical vibrations by monitoring the angular velocity of a vane suspended in the medium and driven by an external motor. On increasing the frequency, we observe a reentrant transition, as a jammed system first enters a fluidized state, where the vane rotates with high constant velocity, and then returns to a frictional state, where the vane velocity is much lower. While the fluidization frequency is material independent, the viscosity recovery frequency shows a clear dependence on the material that we rationalize by relating this frequency to the balance between dissipative and inertial forces in the system. Molecular dynamics simulations well reproduce the experimental data, confirming the suggested theoretical picture. [ABSTRACT FROM AUTHOR]

According to the acoustic fluidization hypothesis, elastic waves at a characteristic frequency form inside seismic faults even in the absence of an external perturbation. These waves are able to generate a normal stress which contrasts the confining pressure and promotes failure. Here, we study the mechanisms responsible for this wave activation via numerical simulations of a granular fault model. We observe the particles belonging to the percolating backbone, which sustains the stress, to perform synchronized oscillations over ellipticlike trajectories in the fault plane. These oscillations occur at the characteristic frequency of acoustic fluidization. As the applied shear stress increases, these oscillations become perpendicular to the fault plane just before the system fails, opposing the confining pressure, consistently with the acoustic fluidization scenario. The same change of orientation can be induced by external perturbations at the acoustic fluidization frequency. [ABSTRACT FROM AUTHOR]

The unexpected weakness of some faults has been attributed to the emergence of acoustic waves that promote failure by reducing the confining pressure through a mechanism known as acoustic fluidization, also proposed to explain earthquake remote triggering. Here we validate this mechanism via the numerical investigation of a granular fault model system. We find that the stick-slip dynamics is affected only by perturbations applied at a characteristic frequency corresponding to oscillations normal to the fault, leading to gradual dynamical weakening as failure is approaching. Acoustic waves at the same frequency spontaneously emerge at the onset of failure in the absence of perturbations, supporting the relevance of acoustic fluidization in earthquake triggering. [ABSTRACT FROM AUTHOR]

Pattern recognition is a fundamental neuronal process which enables a cortical system to interpret visual stimuli. How the brain learns to recognize patterns is, however, an unsolved problem. The frequently employed method of back propagation excels at this task but has been found to be unbiological in many aspects. In this Rapid Communication we achieve pattern recognition tasks in a biologically, fully consistent framework. We consider a neuronal network exhibiting avalanche dynamics, as observed experimentally, and implement negative feedback signals. These are chemical signals, such as dopamine, which mediate synaptic plasticity and sculpt the network to achieve certain tasks. The system is able to distinguish horizontal and vertical lines with high accuracy, as well as to perform well at the more complicated task of handwritten digit recognition. Resulting from the learning mechanism, spatially separate activity regions emerge, as observed in the primary visual cortex using functional magnetic resonance imaging techniques. The results therefore suggest that negative feedback signals offer an explanation for the emergence of distinct activity areas in the visual cortex. [ABSTRACT FROM AUTHOR]

In recent years self organized critical neuronal models have provided insights regarding the origin of the experimentally observed avalanching behavior of neuronal systems. It has been shown that dynamical synapses, as a form of short-term plasticity, can cause critical neuronal dynamics. Whereas long-term plasticity, such as Hebbian or activity dependent plasticity, have a crucial role in shaping the network structure and endowing neural systems with learning abilities. In this work we provide a model which combines both plasticity mechanisms, acting on two different time scales. The measured avalanche statistics are compatible with experimental results for both the avalanche size and duration distribution with biologically observed percentages of inhibitory neurons. The time series of neuronal activity exhibits temporal bursts leading to 1/f decay in the power spectrum. The presence of long-term plasticity gives the system the ability to learn binary rules such as xor, providing the foundation of future research on more complicated tasks such as pattern recognition. [ABSTRACT FROM AUTHOR]

The identification of patterns in space, time, and magnitude, which could potentially encode the subsequent earthquake magnitude, represents a significant challenge in earthquake forecasting. A pivotal aspect of this endeavor involves the search for correlations between earthquake magnitudes, a task greatly hindered by the incompleteness of instrumental catalogs. A novel strategy to address this challenge is provided by the groundbreaking observation by Van der Elst (Journal of Geophysical Research: Solid Earth, 2021) that positive magnitude differences, under specific conditions, remain unaffected by catalog incompleteness. In this Letter, we apply these conditions and provide clear and compelling evidence for the existence of correlations between consecutive positive magnitude differences. Our findings strongly support the scenario where the distribution of subsequent earthquake magnitudes depends on the magnitude of the triggering earthquake.

The relation between spontaneous and stimulated brain activity is a fundamental question in neuroscience which has received wide attention in experimental studies. Recently, it has been suggested that the evoked response to external stimuli can be predicted from temporal correlations of spontaneous activity. Previous theoretical results, confirmed by the comparison with magnetoencephalography data for human brains, were obtained for the Wilson-Cowan model in the condition of balance of excitation and inhibition, a signature of a healthy brain. Here we extend previous studies to imbalanced conditions by examining a region of parameter space around the balanced fixed point. Analytical results are compared to numerical simulations of Wilson-Cowan networks. We evidence that in imbalanced conditions the functional form of the time correlation and response functions can show several behaviors, exhibiting also an oscillating regime caused by the emergence of complex eigenvalues. The analytical predictions are fully in agreement with numerical simulations, validating the role of cross-correlations in the response function. Furthermore, we identify the leading role of inhibitory neurons in controlling the overall activity of the system, tuning the level of excitability and imbalance.

Many systems in nature exhibit avalanche dynamics with scale-free features. A general scaling theory has been proposed for critical avalanche profiles in crackling noise, predicting the collapse onto a universal avalanche shape, as well as the scaling behavior of the activity power spectrum as Brown noise. Recently, much attention has been given to the profile of neuronal avalanches, measured in neuronal systems in vitro and in vivo. Although a universal profile was evidenced, confirming the validity of the general scaling theory, the parallel study of the power spectrum scaling under the same conditions was not performed. The puzzling observation is that in the majority of healthy neuronal systems the power spectrum exhibits a behavior close to 1/f, rather than Brown, noise. Here we perform a numerical study of the scaling behavior of the avalanche shape and the power spectrum for a model of integrate and fire neurons with a short-term plasticity parameter able to tune the system to criticality. We confirm that, at criticality, the average avalanche size and the avalanche profile fulfill the general avalanche scaling theory. However, the power spectrum consistently exhibits Brown noise behavior, for both fully excitatory networks and systems with 30% inhibitory networks. Conversely, a behavior closer to 1/f noise is observed in systems slightly off criticality. Results suggest that the power spectrum is a good indicator to determine how close neuronal activity is to criticality.

Local anaxonic neurons with graded potential release are important ingredients of nervous systems, present in the olfactory bulb system of mammalians and in the human visual system, as well as in arthropods and nematodes. We develop a neuronal network model including both axonic and anaxonic neurons and monitor the activity tuned by the following parameters: the decay length of the graded potential in local neurons, the fraction of local neurons, the largest eigenvalue of the adjacency matrix, and the range of connections of the local neurons. Tuning the fraction of local neurons, we derive the phase diagram including two transition lines: a critical line separating subcritical and supercritical regions, characterized by power-law distributions of avalanche sizes and durations, and a bifurcation line. We find that the overall behavior of the system is controlled by a parameter tuning the relevance of local neuron transmission with respect to the axonal one. The statistical properties of spontaneous activity are affected by local neurons at large fractions and on the condition that the graded potential transmission dominates the axonal one. In this case the scaling properties of spontaneous activity exhibit continuously varying exponents, rather than the mean-field branching model universality class.

Particle detachment bursts during the flow of suspensions through porous media are a phenomenon that can severely affect the efficiency of deep bed filters. Despite the relevance in several industrial fields, little is known about the statistical properties and the temporal organization of these events. We present experiments of suspensions of deionized water carrying quartz particles pushed with a peristaltic pump through a filter of glass beads measuring simultaneously the pressure drop, flux, and suspension solid fraction. We find that the burst size distribution scales consistently with a power law, suggesting that we are in the presence of a novel experimental realization of a self-organized critical system. Temporal correlations are present in the time series, like in other phenomena such as earthquakes or neuronal activity bursts, and also an analog to Omori's law can be shown. The understanding of burst statistics could provide novel insights in different fields, e.g., in the filter and petroleum industries.

We present a study of the earthquake intertime distribution D(Δt) for a California catalog in temporal periods of short duration T. We compare experimental results with theoretical predictions and analytical approximate solutions. For the majority of intervals, rescaling intertimes by the average rate leads to collapse of the distributions D(Δt) on a universal curve, whose functional form is well fitted by a Gamma distribution. The remaining intervals, exhibiting a more complex D(Δt), are all characterized by the presence of large shocks. These results can be understood in terms of the relevance of the ratio between the characteristic time c in the Omori law and T: Intervals with Gamma-like behavior are indeed characterized by a vanishing c/T. The above features are also investigated by means of numerical simulations of the Epidemic Type Aftershock Sequence (ETAS) model. This study shows that collapse of D(Δt) is also observed in numerical catalogs; however, the fit with a Gamma distribution is possible only assuming that c depends on the main-shock magnitude m. This result confirms that the dependence of c on m, previously observed for m>6 main shocks, extends also to small m>2.

Neuronal avalanches, measured in vitro and in vivo, exhibit a robust critical behavior. Their temporal organization hides the presence of correlations. Here we present experimental measurements of the waiting time distribution between successive avalanches in the rat cortex in vitro. This exhibits a nonmonotonic behavior not usually found in other natural processes. Numerical simulations provide evidence that this behavior is a consequence of the alternation between states of high and low activity, named up and down states, leading to a balance between excitation and inhibition controlled by a single parameter. During these periods, both the single neuron state and the network excitability level, keeping memory of past activity, are tuned by homeostatic mechanisms.

One of the challenges in fighting cybercrime is to understand the dynamics of message propagation on botnets, networks of infected computers used to send viruses, unsolicited commercial emails (SPAM) or denial of service attacks. We map this problem to the propagation of multiple random walkers on directed networks and we evaluate the interarrival time distribution between successive walkers arriving at a target. We show that the temporal organization of this process, which models information propagation on unstructured peer to peer networks, has the same features as SPAM reaching a single user. We study the behavior of the message interarrival time distribution on three different network topologies using two different rules for sending messages. In all networks the propagation is not a pure Poisson process. It shows universal features on Poissonian networks and a more complex behavior on scale free networks. Results open the possibility to indirectly learn about the process of sending messages on networks with unknown topologies, by studying interarrival times at any node of the network.

A major issue in biology is the understanding of the interactions between proteins. These interactions can be described by a network, where the proteins are modeled by nodes and the interactions by edges. The origin of these protein networks is not well understood yet. Here we present a two-step model, which generates clusters with the same topological properties as networks for protein-protein interactions, namely, the same degree distribution, cluster size distribution, clustering coefficient, and shortest path length. The biological and model networks are not scale-free but exhibit small-world features. The model allows the fitting of different biological systems by tuning a single parameter.

The unjamming transition of granular systems is investigated in a seismic fault model via three dimensional molecular dynamics simulations. A two-time force-force correlation function, and a susceptibility related to the system response to pressure changes, allow us to characterize the stick-slip dynamics, consisting in large slips and microslips leading to creep motion. The correlation function unveils the micromechanical changes occurring both during microslips and slips. The susceptibility encodes the magnitude of the incoming microslip.

The interevent time distribution characterizes the temporal occurrence in seismic catalogs. Universal scaling properties of this distribution have been evidenced for entire catalogs and seismic sequences. Recently, these universal features have been questioned and some criticisms have been raised. We investigate the existence of universal scaling properties by analyzing a Californian catalog and by means of numerical simulations of an epidemic-type model. We show that the interevent time distribution exhibits a universal behavior over the entire temporal range if four characteristic times are taken into account. The above analysis allows us to identify the scaling form leading to universal behavior and explains the observed deviations. Furthermore, it provides a tool to identify the dependence on the mainshock magnitude of the c parameter that fixes the onset of the power law decay in the Omori law.

We investigate the spatial distribution of aftershocks, and we find that aftershock linear density exhibits a maximum that depends on the main shock magnitude, followed by a power law decay. The exponent controlling the asymptotic decay and the fractal dimensionality of epicenters clearly indicate triggering by static stress. The nonmonotonic behavior of the linear density and its dependence on the main shock magnitude can be interpreted in terms of diffusion of static stress. This is supported by the power law growth with exponent H approximately 0.5 of the average main-aftershock distance. Implementing static stress diffusion within a stochastic model for aftershock occurrence, we are able to reproduce aftershock linear density spatial decay, its dependence on the main shock magnitude, and its evolution in time.

A crucial point in the debate on the feasibility of earthquake predictions is the dependence of an earthquake magnitude from past seismicity. Indeed, while clustering in time and space is widely accepted, much more questionable is the existence of magnitude correlations. The standard approach generally assumes that magnitudes are independent and therefore in principle unpredictable. Here we show the existence of clustering in magnitude: earthquakes occur with higher probability close in time, space, and magnitude to previous events. More precisely, the next earthquake tends to have a magnitude similar but smaller than the previous one. A dynamical scaling relation between magnitude, time, and space distances reproduces the complex pattern of magnitude, spatial, and temporal correlations observed in experimental seismic catalogs.

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Moreover, experimental studies of morphology indicate that neurons develop a network of small-world-like connections, with the possibility of a very high connectivity degree. Here we study a recent model based on self-organized criticality, which consists of an electrical network with threshold firing and activity-dependent synapse strengths. We study the model on a scale-free network, the Apollonian network. The system exhibits an avalanche activity with a power law distribution of sizes and durations. The analysis of the power spectra of the electrical signal reproduces very robustly the power law behavior with the exponent 0.8, experimentally measured in electroencephalogram spectra. The exponents are found to be quite stable with respect to initial configurations and strength of plastic remodeling, indicating that universality holds for a wide class of neural network models.

We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this scaling hypothesis. We present a numerical protocol able to generate a synthetic catalog with an arbitrary large number of events. The numerical data reproduce the hierarchical organization in time and magnitude of experimental interevent time distribution.

Earthquakes and solar flares are phenomena involving huge and rapid releases of energy characterized by complex temporal occurrence. By analyzing available experimental catalogs, we show that the stochastic processes underlying these apparently different phenomena have universal properties. Namely, both problems exhibit the same distributions of sizes, interoccurrence times, and the same temporal clustering: We find after flare sequences with power law temporal correlations as the Omori law for seismic sequences. The observed universality suggests a common approach to the interpretation of both phenomena in terms of the same driving physical mechanism.

The increase in viscosity that is observed in attractive colloidal systems by varying the temperature or the volume fraction can be related to the formation of structures due to particle aggregation. In particular we have studied the nontrivial dependence of the viscosity from the temperature and the volume fraction in the copolymer-micellar system L64. The comparison of the experimental data with the results of numerical simulations in a simple model for gelation phenomena suggests that this intriguing behavior can be explained in terms of cluster formation and that this picture can be quite generally extended to other attractive colloidal systems.

Networks of living neurons exhibit an avalanche mode of activity, experimentally found in organotypic cultures. Here we present a model that is based on self-organized criticality and takes into account brain plasticity, which is able to reproduce the spectrum of electroencephalograms (EEG). The model consists of an electrical network with threshold firing and activity-dependent synapse strengths. The system exhibits an avalanche activity in a power-law distribution. The analysis of the power spectra of the electrical signal reproduces very robustly the power-law behavior with the exponent 0.8, experimentally measured in EEG spectra. The same value of the exponent is found on small-world lattices and for leaky neurons, indicating that universality holds for a wide class of brain models.

We here discuss the results of three-dimensional Monte Carlo simulations of a minimal lattice model for gelling systems. We focus on the dynamics investigated by means of the time autocorrelation function of the density fluctuations and the particle mean-square displacement. We start from the case of chemical gelation, i.e., with permanent bonds, and characterize the critical dynamics as determined by the formation of the percolating cluster, as actually observed in polymer gels. By opportunely introducing a finite bond lifetime tau(b), the dynamics displays relevant changes and eventually the onset of a glassy regime. This has been interpreted in terms of a crossover to dynamics more typical of colloidal systems and a connection between classical gelation and recent results on colloidal systems is suggested. By systematically comparing the results in the case of permanent bonds to finite bond lifetime, the crossover and the glassy regime can be understood in terms of effective clusters.

The elastic response in polymeric gels is studied by means of a percolation dynamic model. By numerical simulations the fluctuations in the gyration radius and in the center-of-mass motion of the percolating cluster are determined. Their scaling behavior at the gelation threshold gives a critical exponent for the elastic modulus f approximately 2.5+/-0.1 in agreement with the prediction f=dnu.